Why was it necessary for Travis to break eggs in front of Old Yeller?

Travis wanted to prove that Old Yeller was stealing the eggs.... but Old Yeller wasn't letting him prove anything....

I called Old Yeller off from the house and broke the eggs on a flat rock, right under his nose and tried to get him to eat them. But he wouldn’t. He acted like he’d never heard tell that eggs were fit to eat. All he’d do was stand there and wiggle his tail and try to lick me in the face